Processing local-stationary data amounts to splitting, processing, and then merging stationary patches. The idea of patching is easily explained but its software implementation is tricky.
I redesigned Claerbout's original approach Claerbout (1992b) in an object-oriented framework. Due to Jest's handling of domain and range, the patch operators yield a high-level user interface that simply requires patch specifications and an operator factory object. The patches are specified by patch size and overlap in the domain or range. The operator factory generates a stationary operator given a specific domain and range patch.
Alternative approaches to process local-stationary data exist. In particular, I considered Claerbout's formulation of an underdetermined inverse problem that estimates an operator for each input sample. The discussion of filter versus data interpolation, discussed above, indicates that, for slowly varying local-stationary data, such a variable operator approach is equivalent to the chapter's patching scheme.